OFFSET
1,6
LINKS
Kenny Lau, Table of n, a(n) for n = 1..553
EXAMPLE
A(x) = x + x^2 + x^5 - 3*x^6 + 7*x^7 - 10*x^8 - 5*x^9 +...
where A(A(x)) = x + 2*x^2 + 2*x^3 + x^4 + 2*x^5 + x^6 +... is the g.f. of A112104.
MATHEMATICA
kmax = 40;
A[x_] := Sum[a[k] x^k, {k, kmax}];
B[x_] := Sum[b[k] x^k, {k, kmax}];
sol = {a[1] -> 1, b[1] -> 1};
Do[sc = SeriesCoefficient[A[(A[x] /. sol) + O[x]^(k+1)] - B[x], {x, 0, k}] /. sol; r = Reduce[(b[k] == 1 || b[k] == 2) && sc == 0, {a[k], b[k]}, Integers]; sol = Join[r // ToRules, sol], {k, 2, kmax}];
a /@ Range[kmax] /. sol (* Jean-François Alcover, Nov 05 2019 *)
PROG
(PARI) {a(n, m=2)=local(F=x+x^2+x*O(x^n), G); if(n<1, 0, for(k=3, n, G=F+x*O(x^k); for(i=1, m-1, G=subst(F, x, G)); F=F-((polcoeff(G, k)-1)\m)*x^k); return(polcoeff(F, n, x)))}
CROSSREFS
KEYWORD
sign
AUTHOR
Paul D. Hanna, Aug 27 2005
STATUS
approved